Dynamics of a Lightning Channel Corona Sheath Using a Generalized Traveling-Current-Source Return Stroke Model—Theory and Calculations

Abstract-A generalized lightning traveling-current-source return stroke model (GTCS) and the measurements of Miki et al. [J. Geophys. Res., vol. 107, no. D16, pp. ACL2.1-ACL2.11, 2002], are used to calculate the dynamics of a lightning channel corona sheath surrounding a thin channel core during the return stroke stage. The channel corona sheath model that predicts the charge motion in the corona sheath is used to determine the corona sheath dynamics. This model can be viewed as the generalization of the corona sheath model proposed by Maslowski and Rakov [J. Geophys. Res., vol. 111, D14110, pp. 1-16, 2006]. According to this model, the corona sheath surrounding the thin channel core consists of two zones containing charge, zone 1 (inner zone containing net positive charge) and zone 2 (zone containing negative charge surrounding zone 1), respectively, and an outer zone 3 surrounding zone 2 without charge. Theoretical expressions for the corona sheath radii and the velocities of both zones are derived. Using a theoretical expression for the radial electric field in the immediate vicinity of the channel core derived for the GTCS model and the measured electric field waveforms of Miki et al. [J. Geophys. Res., vol. 107, no. D16, pp. ACL2.1-ACL2.11, 2002], the channel discharge function versus time is calculated. Based on this function and the measured channel-base current function, the corona sheath radii of both zones and their velocities versus time in the bottom portion of the channel are calculated. It is shown that the maximum radii of zones 1 and 2 at 2 m above ground are less than 1.5 and 6 cm, respectively. Corresponding maximum radial corona sheath velocities are less than 6 × 10
⁴
m/s. Small values of the maximum radii of zones 1 and 2 can be explained by the small value of the channel line charge density of 6.7 μC/m, due to vicinity of perfect ground. Using measured channel-base current and the calculated channel discharge function, the line charge distribution versus height is calculated. The current reflections from the striking point are considered. For the ground current reflection factor R = 1 (the reflection from the perfectly conducting ground) the peak value of the channel line charge density is 0.75 mC/m at the height of about 12 m above ground and for R = 0 (no current reflections) the peak value is 1.3 mC/m, at about 17 m above ground. The corresponding calculated values of the return stroke velocities in the channel bottom are 1.29 × 10
⁸
m/s (0.43c) and 1.68 × 10
⁸
m/s (0.56c), respectively. The corona sheath expansion velocity is about three orders of magnitude less than the calculated lightning return stroke velocity. The result concerning the channel line charge distribution is in the agreement with the measurements of Crawford et al. [J. Geophys. Res., vol. 106, pp. 14909-14917, 2001], whereas the calculated return stroke velocities are in a good agreement with the optical measurements of Willet et al. [J. Geophys. Res., vol. 93, pp. 3867-3878, 1988] and [J. Geophys. Res., vol. 94, pp. 1327513286,1989].